Web Content Accessibility Guide (WCAG 2.0) is divided into three conformance levels (A, AA, and AAA).
They are organized based on the impact they have on design or visual presentation of the pages. The higher the level, the more restraining it becomes on design. As a rule of thumb, success criteria from level A should be invisible or barely noticeable to the interface. On the other hand, level AAA will have such a high impact on design, that most organizations will not be able to achieve that level (as the compromises on design will be too important).
I recommend a goal of AA conformance, with the understanding that 100% conformance is only goal and is typically very difficult to achieve. This is the same recommendation the W3 organization makes as well.
For UX accessibility and conformance to both WCAG 2.0 and Section 508 we can use an node.js tool called Pa11y. Pa11y is a free tool that produces a report of any compliance issues for any website. This tool can be run on developers machines and your build server so that each time a developer changes code, the tool automatically produces a report of which items are not in compliance and at what level they are. The tool is very fast, less than a few seconds for any page.
In practice, the way it works best is: